Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002


Nodal domains of graphs


Türker Biyikoglu


Department for Applied Statistics and Data Processing, University of Economics and Business Administration, Augasse 2-6, A-1090 Vienna, Austria



Let f be a real function on the vertices of a graph G = 3D(V, E). A strong (weak) nodal domain of f is a maximal connected induced subgraph G[W] of G with vertex set W such that f(x)f(y) > 0 (f(x)f(y 0) for all x, y Î W. I will talk about the number of strong and weak nodal domains of some graph classes, where the function f is an eigenvector of Laplace matrix (Schrödinger operator) of a graph. These eigenvectors are of interest in simplified quantum mechanical models of organic molecules.